In recent years there has been increased research activity in the area of Func-
tional Data Analysis. Methodology from finite dimensional multivariate analysis has
been extended to the functional data setting giving birth to Functional ANOVA,
Functional Principal Components Analysis, etc. In particular, some studies have pro-
posed inferential techniques for various functional models that have connections to
well known areas such as mixed-effects models or spline smoothing. The methodol-
ogy used in these cases is computationally intensive since it involves the estimation of
coefficients in linear models, adaptive selection of smoothing parameters, estimation
of variances components, etc.
This dissertation proposes a wide-ranging modeling framework that includes
many functional linear models as special cases. Three widely used tools are con-
sidered: mixed-effects models, penalized least squares, and Bayesian prediction. We
show that, in certain important cases, the same numerical answer is obtained for these
seemingly different techniques. In addition, under certain assumptions, an applica-
tion of a Kalman filter algorithm is shown to improve the order of computations, by
two orders of magnitude, for point and interval estimates (with n being the sample
size). A functional data analysis setting is used to exemplify our results.
| Identifer | oai:union.ndltd.org:tamu.edu/oai:repository.tamu.edu:1969.1/2637 |
| Date | 01 November 2005 |
| Creators | Munoz Maldonado, Yolanda |
| Contributors | Eubank, Randall L. |
| Publisher | Texas A&M University |
| Source Sets | Texas A and M University |
| Language | en_US |
| Detected Language | English |
| Type | Book, Thesis, Electronic Dissertation, text |
| Format | 746210 bytes, electronic, application/pdf, born digital |
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